Exploiting a three-band Hamiltonian model [1]}, [2]}, [3]}, [4]}, [5]}, [6]} and the NEGF method, besides the spin polarization studies in lateral two- dimensional \(MoS(Se)_{2}-WS(Se)_{2}\)  TMD heterostructures, it has been shown, at the two K and K’ corners of first Brillouin zone (BZ), the Bloch states in monolayer \(MX_{2}\)  (M=Mo, W and X=S, Se) mostly consist of \(d_{{z}^{2}}\)  orbitals for the conduction band minimum (CBM), and \(d_{xy}\)  and \(d_{{x}^{2}-{y}^{2}}\)  for the valence band maximum (VBM) [7]}, [8]}, [9]}, [10]}, [11]}, [12]}. Additional information including the hopping matrix between metal atoms in each displacement direction and on-site matrix of each metal atom is provided in appendix .
In order to calculate the spin polarization and spin current which are defined as Eq.REF  and Eq.REF  respectively, one should evaluate the transmission probability, T +(-), of spin up (down) electrons through the NEGF method [13]}, [14]}, [15]}, [16]}.
\({SP=\frac{T^{+}-T^{-}}{T^{+}+T^{-}}} \) 
\({I}^{+(-)}(E,V)=\frac{q}{\pi {}\hbar {}}\int {T}^{+(-)}(E,V)[\mathit {f}_{1}(E,V)-\mathit {f}_{2}(E,V)]dE \) 
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